Is anybody still using Conceptual Dependency Theory?
Although this model played an important role in contributing  to our present understanding of NLP and NLU, it is no longer useful in production systems and currently no successful commercial product follows this approach. 

In CDT the goal was to design an AI system that could draw logical inferences from sentences. In this system the goal was to make the meaning independent of the words used in the input.  

CDT modeled sentences by using tokens such as: locations, time, real world actions and real world objects. However as computational power became more common and less expensive, interest diverted to statistical models which were now outperforming the previous rule based systems.  

The problem with rule based approaches such as CDT is that they require manual development of linguistic rules which can be costly and which usually don't generalize well to other languages.

On the other hand, statistical approaches use  human language resources (multilingual textual corpora) more efficiently. Rather than using a rule based approach, statistical models make soft probabilistic decisions based on attaching real weights to the features making up the input data. (Wikipedia NLP)

This efficient use of human language resources leads to a model that is more accurate and robust especially when given unfamiliar input or input that contains errors. Statistical models also generalise well to other languages.